200 PROPAGATION OF ELECTRICITY. 



and electrical conductivity. These three flows are therefore pro- 

 portional to each other. 



According to this, whenever a problem of the uniform propa- 

 gation of heat or of statical electricity has been solved, the 

 corresponding problem of the propagation of electricity in the 

 permanent state, will be found to be solved in the same way. 



As a particular case, we have seen that if we assign the potentials 

 V lf V 2 . . , V n to fixed surfaces S 1} S 2 . . , S n that is to say, the poten- 

 tials of different conductors in air the potential at every point of the 

 medium is defined, and the problem of equilibrium has only one 

 solution. In like manner, if the dielectric medium is replaced by a 

 conductor, and the potentials are kept constant on the same surfaces 

 Sj, S 2 . . . S n , the flow of electricity is determined for each point, and 

 there is only a single state of equilibrium. 



213. Suppose now that two dielectrics, whose inductive capacities 

 are /^ and /x 2 , are separated by a surface S. The flow of force is not 

 maintained on each side of the surface, but the flow of induction is 

 maintained, and counting the normal n to the surface in the same 

 direction for the two media, we have (121) 



C.L.COHY. 3V w . 



It is the condition of continuity on the surface. If we replace the 

 dielectrics by conductors whose coefficients of conductivity are ^ and 

 c^ the flow of electricity is then the same on each side of the surface 

 S, which gives 



W <>V 2 



It will be seen from this that if, in a problem of electrostatics 

 containing dielectrics whose inductive capacities are yu 15 //. 2 , . . //, 3 , we 

 replace 4he dielectrics by conductors whose coefficients of conduc- 

 tivity are respectively proportional to the corresponding inductive 

 capacities, such, that is to say, that we have 



the flow of electricity at each point will be proportional to the flow 

 of induction of the correlated electrostatic system. 



